Of course it will not make your get the dark circles under your eyes. It will make you feel good when you rub your tired eyes. Because in everyday life, we just have to open our eyes to look at things and some people who have a job which are associated with the computer are even worse. They make their eyes too pressed. When you rub your eyes, just like you have massage for your body, it will improve the blood flow. In this way, your eyes nerve can be relaxed so in the end your eyes and even your body will feel comfortable. But on the other hand, to make your eyes healthy, you should not overuse your eyes and make sure to have a good rest.
No, it will not cause the dark circles under the eyes just by rubbing your eyes in the normal situation. The dark circles are caused by the lack of sleep, lack of vitamin C or stay up at night. If you just rub your eye, you may get the infection on the eyes because of the invisible bacterium getting through in your eyes.
Nope, it could not cause that. Because dark circles could point towards a weak function of liver or kidney that not as desired. Many who suffer from sinus problems could develop dark circles under the eyes. If the dark circles are caused due to some medical condition, you will know it, because the dark circles will be just one out of possibly many symptoms caused. On the other side, dark circles could appear when you keep aging. The prime culprit almost always are the veins beneath the skin under the eye which is very thin. This skin is very easily damaged and is always the first to show. Aging and damage caused by the sun make the skin thin and translucent, allowing the veins beneath very prominent. These veins are what make the skin look dark. The skin also looks baggy and puffed because elasticity of the skin keeps reducing with age.